Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
n = int(input())
v = math.floor((-1 + math.sqrt(1 + 8 * n)) / 2)
for i in range(v, 0, -1):
	z = n - i * (i + 1) / 2
	# 2z=a*(a+1) a^2+a-2z=0
	a = (-1 + math.sqrt(1 + 8 * z)) / 2
	if a.is_integer() and a > 0:
		print("YES")
		exit(0)
print("NO")